KEYWORDS: Phase imaging, Holography, Contrast transfer function, Super resolution, Microscopy, Image resolution, Diffraction, Transmittance, Phase shifts, Near field diffraction
Quantitative phase imaging (QPI) has emerged as a powerful computational tool that enables imaging unla- belled specimens with high contrast. It finds applications in microscopy, refractive index mapping , biomedical imaging and surface measurement. Several techniques including interferometry, holography, iterative methods and Transport of Intensity Equation have been developed over the years for QPI. However, the spatial resolution of the retrieved phase images are limited by the diffraction limit of the imaging system. Prior work on Super resolution phase imaging has been primarily focused on holography based techniques which require illumination sources with high coherence , phase unwrapping and high experimental stability. In this work, we propose a propagation based super resolution phase imaging technique using Contrast Transfer Function(CTF) and structured illumination. An enhancement in resolution by two folds is demonstrated using numerical results.
Structured illumination (SI) phase imaging is an important strategy to achieve quantitative phase imaging via encoding phase-induced diffraction into modulation intensity signals through propagation. However, the nonlinear property of SI-based transfer function results in ill-posedness in phase imaging retrieval. Overlapping modulation spectrum usually leads to loss of high spatial frequency components. Recent studies show that such nonlinear inversion problems can be efficiently represented by deep neural networks, as have been demonstrated in phase retrieval via holography and Fourier ptychography techniques. Here we present a hierarchical synthesis network (HSNet) which uses multiple splitting networks to extract structural features of structured intensity images in various modulation frequency and synthesis network to produce high fidelity reconstruction. We show that the proposed framework retrieve clear and accurate phase profile with reduced computing requirements in simulation.
KEYWORDS: Image resolution, Signal to noise ratio, Phase imaging, Signal processing, Diffraction, Phase shift keying, Optical transfer functions, Modulation, Filtering (signal processing), Digital filtering
Transport of Intensity equation(TIE) is a non-interferometric method used for quantitative phase imaging. By reformulating the TIE using Contrast Transfer Function, it can be determined that the spatial resolution of the phase retrieved using TIE is limited by the product of imaging system transfer function and a sinc function. In this work, we apply the principles of structured illumination fluorescent microscopy to develop a TIE based super resolved phase imaging technique. The sinusoidal intensity pattern down modulates high frequency spectrum of the phase into the system pass band thereby providing a convenient approach to synthetically enlarge the numerical aperture of the system. Resolution enhancement by two folds is demonstrated using simulations.
Transport of Intensity Equation (TIE) is a powerful computational tool for quantitative phase imaging using intensity only measurement. However, one drawback of TIE is that it does not include any parameters of the imaging system in the equation. To account for the effect of the imaging system on the retrieved phase, TIE is reformulated using Contrast Transfer Function (CTF) to analytically derive the distortion functions present in TIE. The distortion function attenuates the frequency components in the pass band resulting in a blurry phase image. For image restoration, signal parameters are estimated by minimizing a cost function for power spectrum and an optimal wiener filter is employed to deconvolve the distortion function. The proposed method is experimentally demonstrated through a visible enhancement in the phase images of human cheek cells obtained using a bright field microscope.
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